MathDB

1

Part of 2022 New Zealand MO

Problems(2)

<PCB =? ABCD rectangle 1x2, MBP equilateral. AM=//MD

Source: 2022 NZMO - New Zealand Maths Olympiad Round 1 p1

10/9/2022
ABCDABCD is a rectangle with side lengths AB=CD=1AB = CD = 1 and BC=DA=2BC = DA = 2. Let M M be the midpoint of ADAD. Point PP lies on the opposite side of line MBMB to AA, such that triangle MBPMBP is equilateral. Find the value of ∠PCB\angle PCB.
geometryrectangleEquilateralangles
a^2 + b = b^{2022} diophantine

Source: 2022 NZMO - New Zealand Maths Olympiad Round 2 p1

10/8/2022
Find all integers a,ba, b such that a2+b=b2022.a^2 + b = b^{2022}.
number theoryDiophantine equationdiophantine